VPSim: Variance propagation by simulation

摘要

One of the fundamental concepts in a materials control and accountability system for nuclear safeguards is the materials balance (MB). All transfers into and out of a material balance area are measured, as are the beginning and ending inventories. The resulting MB measures the material loss, MB = T(sub in) + I(sub B) (minus) T(sub out) (minus) I(sub E). To interpret the MB, the authors must estimate its measurement error standard deviation, (sigma)(sub MB). When feasible, they use a method usually known as propagation of variance (POV) to estimate (sigma)(sub MB). The application of POV for estimating the measurement error variance of an MB is straightforward but tedious. By applying POV to individual measurement error standard deviations they can estimate (sigma)(sub MB) (or more generally, they can estimate the variance-covariance matrix, (Sigma), of a sequence of MBs). This report describes a new computer program (VPSim) that uses simulation to estimate the (Sigma) matrix of a sequence of MBs. Given the proper input data, VPSim calculates the MB and (sigma)(sub MB), or calculates a sequence of n MBs and the associated n-by-n covariance matrix, (Sigma). The covariance matrix, (Sigma), contains the variance of each MB in the diagonal entries and the covariance between pairs of MBs in the off-diagonal entries.